Related papers: Only Classical Parameterised States have Optimal M…
Estimation of quantum states and measurements is crucial for the implementation of quantum information protocols. The standard method for each is quantum tomography. However, quantum tomography suffers from systematic errors caused by…
We introduce an operational and statistically meaningful measure, the quantum tomographic transfer function, that possesses important physical invariance properties for judging whether a given informationally complete quantum measurement…
Quantum state verification provides an efficient approach to characterize the reliability of quantum devices for generating certain target states. The figure of merit of a specific strategy is the estimated infidelity $\epsilon$ of the…
In the absence of experimental constraints, optimal measurement schemes for quantum state tomography are well understood. We consider the scenario where the experimenter doesn't have arbitrary freedom to construct their measurement set, and…
Quantum measurements are not deterministic. For this reason quantum measurements are repeated for a number of shots on identically prepared systems. The uncertainty in each measurement depends on the number of shots and the expected outcome…
The estimation of high dimensional quantum states is an important statistical problem arising in current quantum technology applications. A key example is the tomography of multiple ions states, employed in the validation of state…
Quantum state tomography is an integral part of quantum computation and offers the starting point for the validation of various quantum devices. One of the central tasks in the field of state tomography is to reconstruct with high fidelity,…
Entangled multi-photon states have the potential to provide improved measurement accuracy, but are sensitive to photon loss. It is possible to calculate ideal loss-resistant states that maximize the Fisher information, but it is unclear how…
Information plays an important role in our understanding of the physical world. We hence propose an entropic measure of information for any physical theory that admits systems, states and measurements. In the quantum and classical world,…
The quantum Fisher information of a quantum state with respect to a certain parameter quantifies the sensitivity of the quantum state to changes in that parameter. Maximizing the quantum Fisher information is essential for achieving the…
We study the connection between exceptional points (EPs) and optimal parameter estimation, in a simple system consisting of two counter-propagating traveling wave modes in a microring resonator. The unknown parameter to be estimated is the…
We consider highly inaccurate measurements made on classical stochastic and quantum systems. In the quantum case such a \e{weak} measurement preserves coherence between the system's alternatives. We demonstrate that in both cases the…
Optimal state estimation for linear discrete-time systems is considered. Motivated by the literature on differential privacy, the measurements are assumed to be corrupted by Laplace noise. The optimal least mean square error estimate of the…
Markov parameters play a key role in system identification. There exists many algorithms where these parameters are estimated using least-squares in a first, pre-processing, step, including subspace identification and multi-step…
A core principle of quantum theory is that non-orthogonal quantum states cannot be perfectly distinguished with single-shot measurements. However, it is possible to exclude a subset of non-orthogonal states without error in certain…
We consider realistic measurement systems, where measurements are accompanied by decoherence processes. The aim of this work is the construction of methods and algorithms for precise quantum measurements with fidelity close to the…
Measurement is integral to quantum information processing and communication; it is how information encoded in the state of a system is transformed into classical signals for further use. In quantum optics, measurements are typically…
This tutorial introduces a systematic approach for addressing the key question of quantum metrology: For a generic task of sensing an unknown parameter, what is the ultimate precision given a constrained set of admissible strategies. The…
We address the "major open problem" of evaluating how much increased efficiency in estimation is possible using non-separable, as opposed to separable, measurements of N copies of m-level quantum systems. First, we study the six cases m =…
We provide optimal measurement schemes for estimating relative parameters of the quantum state of a pair of spin systems. We prove that the optimal measurements are joint measurements on the pair of systems, meaning that they cannot be…